Auto

Libraries

# Libraries ----
library(readxl) # read exlce
library(dplyr) # For table manipulations
library(plyr) # For table manipulations
library(reshape2) # For melt function to chane data frames to parse into ggplot functions
library(ggplot2) # For Nice plots

Functions

# General functions call
source("functions.R")
# GLM - parameters

# Call the GLM.R script, estimates number and AAC for current automoblies. Also
source("GLM.R")

## readxl works best with a newer version of the tibble package.
## You currently have tibble v1.4.2.
## Falling back to column name repair from tibble <= v1.4.2.
## Message displays once per session.

Base Scenario

Insert initial variables

time.frame <- 0:20
start.year <- 2019
t <- seq(min(time.frame), max(time.frame), by = 0.25)

Safelife marketshare

A0 <- 0.34 + 0.005*t
A1 <- exp(-t*0.2)*0.6 +0.4
A2<- exp(-t*0.19)*0.6 +0.4

safelife.market.share <- data.frame(time = t,
                                    A0 = A0,
                                    A1 = A1,
                                    A2 = A2)

m.safe <- melt(data = safelife.market.share, id = "time")

ggplot(data = m.safe) + geom_line(mapping = aes(x = time, y = value, color = variable)) + 
  scale_x_continuous(name ="Year", breaks = c(time.frame), label = as.character(2019 + time.frame), expand = c(0,0)) +
   scale_y_continuous(name ="Percentage", breaks = c(0, 0.2, 0.4, 0.6, 0.8, 1), label = c("0%", "20%","40%", "60%", "80%", "100%"), limits = c(0,1), expand = c(0,0)) + # expand -> y axis begins at 0 strict
    theme(axis.line = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.border = element_blank(),
    plot.background = element_rect(fill =  "#D3D3D3"),
    panel.background = element_rect(fill =  "#D3D3D3"),
    legend.background = element_rect(fill =  "#D3D3D3")) +
  labs(color = "Autonomy") + ggtitle("Safelife marketshare for each autonomy level") 

Carbia market exposure Personal in percetnages

A1 <- function(t){
  if(t<5){
    (exp(0.01*t)-1)*exp((5-t)*0.05)
  }
  else{
    exp(0.01*t)-1
  }
  }
A2 <- function(t){
  if(t<3){
    0
  }else{
    0.0015*(t-3)^2#exp(0.015*(t-3))-1
  }
}
A1 <- Vectorize(FUN = A1, vectorize.args = "t")
A2 <- Vectorize(FUN = A2, vectorize.args = "t")
A0 <- 1-A1(t)-A2(t)
  


carb.personal.pct <- data.frame(time = t,
                                A0 = A0,
                                A1 = A1(t),
                                A2 = A2(t))

m.carb <- melt(data = carb.personal.pct, id.vars = "time")
m.carb$value[m.carb$variable == "A2" & m.carb$value == 0] <- NA


ggplot(data = m.carb) + geom_line(mapping = aes(x = time, y = value, color = variable)) + 
    scale_x_continuous(name ="Year", breaks = c(time.frame), label = as.character(2019 + time.frame)) +
   scale_y_continuous(name ="Percentage", breaks = c(0, 0.2, 0.4, 0.6, 0.8, 1), label = c("0%", "20%","40%", "60%", "80%", "100%"), limits = c(0,1)) +
    theme(axis.line = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank()) +
  labs(color = "Autonomy") + ggtitle("Personal autonomy level proportions in Carbia")

# fix axisx position

Carbia commercial percentages

A1 <- function(t){
  if(t<5){
    (exp(0.012*t)-1)*exp((5-t)*0.05)
  }
  else{
    exp(0.012*t)-1
  }
  }
A2 <- function(t){
  if(t<3){
    0
  }else{
    0.0025*(t-3)^2#exp(0.015*(t-3))-1
  }
}
A1 <- Vectorize(FUN = A1, vectorize.args = "t")
A2 <- Vectorize(FUN = A2, vectorize.args = "t")
A0 <- 1-A1(t)-A2(t)

carb.commercial.pct <- data.frame(time = t,
                                A0 = A0,
                                A1 = A1(t),
                                A2 = A2(t))

m.carb <- melt(data = carb.commercial.pct, id.vars = "time")
m.carb$value[m.carb$variable == "A2" & m.carb$value == 0] <- NA
#m.carb$variable <- factor(m.carb$variable, levels = c("A2", "A1", "A0"), ordered = T)

#ggplot(data = m.carb) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + 
 # scale_fill_manual(values=c("#027984", "#0d0284", "#0755c1"))
ggplot(data = m.carb) + geom_line(mapping = aes(x = time, y = value, color = variable)) + 
      scale_x_continuous(name ="Year", breaks = c(time.frame), label = as.character(2019 + time.frame)) +
   scale_y_continuous(name ="Percentage", breaks = c(0, 0.2, 0.4, 0.6, 0.8, 1), label = c("0%", "20%","40%", "60%", "80%", "100%"), limits = c(0,1)) +
    theme(axis.line = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank()) +
  labs(color = "Autonomy") + ggtitle("Commercial autonomy level proportions in Carbia")

Carbia total Exposure growth for Commercial and Personal

### Exposure of Personal and Commermcial
mark.share.p <- 0.34
mark.share.c <- 0.34

personal.exposure <- sum(autocar$Exposure[autocar$Year == 2018 & autocar$Qtr == 4 & autocar$Type == "Personal"])/mark.share.p
commercial.exposure <- sum(autocar$Exposure[autocar$Year == 2018 & autocar$Qtr == 4 & autocar$Type == "Commercial"])/mark.share.c 

carbia.exposure <- data.frame(time = t,
                              Personal = personal.exposure*(1+t*0.005),
                              Commercial = commercial.exposure*(1+0.025)^t)


m.carbia.exposure <- melt(data = carbia.exposure, id.vars = c("time"))

ggplot(data = m.carbia.exposure) + geom_line(mapping = aes(x = time, y = value, color = variable)) +
        scale_x_continuous(name ="Year", breaks = c(time.frame), label = as.character(2019 + time.frame)) +
   scale_y_continuous(name ="Exposure") +
    theme(axis.line = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.border = element_blank(),
    panel.background = element_blank()) +
  labs(color = "Type") + ggtitle("Exposure growth in Carbia")

# change to millions 

Frequency and Claim multipliers

# Define as lists, same names 
freq.pct <- list()

freq.pct$A0 <- data.frame(time = t, 
                          NC_BI.pct = rep(1, length(t)), 
                          NC_PD.pct = rep(1, length(t)), 
                          NC_COM.pct = rep(1, length(t)), 
                          NC_COL.pct = rep(1, length(t)), 
                          NC_PI.pct = rep(1, length(t)))

freq.pct$A1 <- data.frame(time = t, 
                          NC_BI.pct = 0.05*(1-carb.personal.pct$A0) + 0.2*carb.personal.pct$A0, 
                          NC_PD.pct = 0.05*(1-carb.personal.pct$A0) + 0.2*carb.personal.pct$A0,
                          NC_COM.pct = rep(1, length(t)), 
                          NC_COL.pct = 0.05*(1-carb.personal.pct$A0) + 0.2*carb.personal.pct$A0,
                          NC_PI.pct = 0.05*(1-carb.personal.pct$A0) + 0.2*carb.personal.pct$A0)

freq.pct$A2 <- data.frame(time = t, 
                          NC_BI.pct = 0.025*(1-carb.personal.pct$A0) + 0.1*carb.personal.pct$A0, 
                          NC_PD.pct = 0.025*(1-carb.personal.pct$A0) + 0.1*carb.personal.pct$A0, 
                          NC_COM.pct = rep(1, length(t)), 
                          NC_COL.pct = 0.025*(1-carb.personal.pct$A0) + 0.1*carb.personal.pct$A0, 
                          NC_PI.pct = 0.025*(1-carb.personal.pct$A0) + 0.1*carb.personal.pct$A0)

loss.pct <- list()
loss.pct$A0 <- data.frame(time = t, 
                          AAC_BI.pct = rep(1, length(t)), 
                          AAC_PD.pct = rep(1, length(t)), 
                          AAC_COM.pct = rep(1, length(t)), 
                          AAC_COL.pct = rep(1, length(t)), 
                          AAC_PI.pct = rep(1, length(t)))

loss.pct$A1 <- data.frame(time = t, 
                          AAC_BI.pct = rep(1, length(t)), 
                          AAC_PD.pct = rep(1, length(t)), 
                          AAC_COM.pct = rep(1.3, length(t)), 
                          AAC_COL.pct = rep(1.3, length(t)), 
                          AAC_PI.pct = rep(1, length(t)))

loss.pct$A2 <- data.frame(time = t, 
                          AAC_BI.pct = rep(1, length(t)), 
                          AAC_PD.pct = rep(1, length(t)), 
                          AAC_COM.pct = rep(1.5, length(t)), 
                          AAC_COL.pct = rep(1.5, length(t)), 
                          AAC_PI.pct = rep(1, length(t)))

Model

time.frame <- time.frame[1:(length(time.frame)-1)]

# interst
bi_i <- glm$rd$Amount$Model$BI$coefficients[names(glm$rd$Amount$Model$BI$coefficients) == "time"]
pd_i <- glm$rd$Amount$Model$PD$coefficients[names(glm$rd$Amount$Model$PD$coefficients) == "time"]
com_i <- glm$rd$Amount$Model$COM$coefficients[names(glm$rd$Amount$Model$COM$coefficients) == "time"]
col_i <- glm$rd$Amount$Model$COL$coefficients[names(glm$rd$Amount$Model$COL$coefficients) == "time"]
pi_i <- glm$rd$Amount$Model$PI$coefficients[names(glm$rd$Amount$Model$PI$coefficients) == "time"]

mean_i <- mean(c(bi_i,pd_i,com_i,col_i,pi_i))

predict.df <- model.2(time.frame = time.frame, autocar = autocar, glm.list = glm$rd, safelife.market.share = safelife.market.share, carbia.exposure = carbia.exposure, carb.commercial.pct = carb.commercial.pct, carb.personal.pct = carb.personal.pct, freq.pct = freq.pct, loss.pct = loss.pct, MR.fac = 0.0255, IS.fac = 0.0127, CR.fac = 0.0764, interest = mean_i ) 
# check if around ~25%
max(predict.df$time)

## [1] 2039

sum(predict.df$Exposure[predict.df$Autonomy != "A0" & predict.df$time == 2030])/sum(predict.df$Exposure[predict.df$time == 2030])

## [1] 0.2638285

plots

plots <- list()

 # remove exposure = 0, but also keep 

predict.df.zero <- predict.df[predict.df$Exposure == 0, ]
 predict.df <- predict.df[predict.df$Exposure != 0, ]

  # Total Exposure Growth
  tmp <- predict.df[, names(predict.df) %in% c("time", "Exposure")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  
  plots$total.exposure <- ggplot(data = tmp) + geom_line(aes(x = time, y = Exposure)) + ggtitle("Total Exposure evolution") + theme(plot.title = element_text(size = 10))

  plots$total.exposure

  # Autonomy evolution
  tmp <- predict.df[, names(predict.df) %in% c("time", "Exposure", "Autonomy")]
  tmp <- aggregate(formula = . ~ time + Autonomy, data = tmp, FUN = sum)
  tmp$Exposure[tmp$Exposure == 0 & tmp$Autonomy == "A2"] <- NA
  plots$Autonomy.evolution <- ggplot(data = tmp) + geom_line(aes(x = time, y = Exposure, color = Autonomy)) + ggtitle("Total Autonomy evolution") + theme(plot.title = element_text(size = 10))
  
  plots$Autonomy.evolution

  # Personal evolution
  tmp <- predict.df[predict.df$Type == "Personal", names(predict.df) %in% c("time", "Exposure", "Autonomy")]
  tmp <- aggregate(formula = . ~ time + Autonomy, data = tmp, FUN = sum)
  tmp$Exposure[tmp$Exposure == 0 & tmp$Autonomy == "A2"] <- NA
  plots$Autonomy.evolution.personal <- ggplot(data = tmp) + geom_line(aes(x = time, y = Exposure, color = Autonomy)) + ggtitle("Total Autonomy evolution for personal") + theme(plot.title = element_text(size = 10))
  
  plots$Autonomy.evolution.personal

  # Commercial evolution
  tmp <- predict.df[predict.df$Type == "Commercial", names(predict.df) %in% c("time", "Exposure", "Autonomy")]
  tmp <- aggregate(formula = . ~ time + Autonomy, data = tmp, FUN = sum)
  plots$Autonomy.evolution.commercial <- ggplot(data = tmp) + geom_line(aes(x = time, y = Exposure, color = Autonomy)) + ggtitle("Total Autonomy commercial") + theme(plot.title = element_text(size = 10))
  
  plots$Autonomy.evolution.commercial

  # PLot the Autonomy evolutions
  
  # multiplot(plots$Autonomy.evolution.personal, plots$Autonomy.evolution, plots$Autonomy.evolution.commercial, cols = 2)
  
  
  # Plot Claims evolution personal
  tmp <- predict.df[, names(predict.df) %in% c("time", "Autonomy", "Type", "NC_BI", "NC_PD", "NC_COM", "NC_COL", "NC_PI", "Exposure")]

  
  tmp <- tmp[, !(names(tmp) %in% "Exposure")]
  
  
  
  tmp <- aggregate(formula = . ~ time + Autonomy + Type, data = tmp, FUN = mean)
  tmp.melt <- melt(data = tmp, id = c("time", "Autonomy", "Type"))
  
  plots$frequency.Personal <- ggplot(data = tmp.melt[tmp.melt$Type == "Personal", ]) + geom_line(mapping = aes(x = time, y = value, color = Autonomy)) + facet_wrap(facets = . ~ variable, scales = "free") + ggtitle("Personal frequency per exposure evolution aggregated With mean")
  
  plots$frequency.Personal

  # plot amount evolution personal
  tmp <- predict.df[, names(predict.df) %in% c("time", "Autonomy", "Type", "AAC_BI", "AAC_PD", "AAC_COM", "AAC_COL", "AAC_PI", "AAC_MR", "AAC_IS", "AAC_CR")]
  tmp <- aggregate(formula = . ~ time + Autonomy + Type, data = tmp, FUN = mean)
  tmp.melt <- melt(data = tmp, id = c("time", "Autonomy", "Type"))
  
  plots$amount.Personal <- ggplot(data = tmp.melt[tmp.melt$Type == "Personal", ]) + geom_line(mapping = aes(x = time, y = value, color = Autonomy)) + facet_wrap(facets = . ~ variable, scales = "free") + ggtitle("Personal mount evolution aggregated With mean")

  plots$amount.Personal

  # Plot Claims evolution Commercial
  tmp <- predict.df[, names(predict.df) %in% c("time", "Autonomy", "Type", "NC_BI", "NC_PD", "NC_COM", "NC_COL", "NC_PI")]
  tmp <- aggregate(formula = . ~ time + Autonomy + Type, data = tmp, FUN = mean)
  tmp.melt <- melt(data = tmp, id = c("time", "Autonomy", "Type"))
  
  plots$frequency.Commercial <- ggplot(data = tmp.melt[tmp.melt$Type == "Commercial", ]) + geom_line(mapping = aes(x = time, y = value, color = Autonomy)) + facet_wrap(facets = . ~ variable, scales = "free") + ggtitle("Commercial frequency evolution aggregated With mean")
  
  plots$frequency.Commercial

  # plot amount evolution Commercial
  tmp <- predict.df[, names(predict.df) %in% c("time", "Autonomy", "Type", "AAC_BI_PV", "AAC_PD_PV", "AAC_COM_PV", "AAC_COL_PV", "AAC_PI_PV")]
  tmp <- aggregate(formula = . ~ time + Autonomy + Type, data = tmp, FUN = mean)
  tmp.melt <- melt(data = tmp, id = c("time", "Autonomy", "Type"))
  
  plots$amount.Commercial <- ggplot(data = tmp.melt[tmp.melt$Type == "Commercial", ]) + geom_line(mapping = aes(x = time, y = value, color = Autonomy)) + facet_wrap(facets = . ~ variable, scales = "free") + ggtitle("Commercial amount evolution aggregated With mean")
  plots$amount.Commercial

  # Plot AC
  tmp <- predict.df[, names(predict.df) %in% c("time", "AC_BI_PV", "AC_PD_PV", "AC_COM_PV", "AC_COL_PV", "AC_PI_PV", "AC_IS_PV", "AC_CR_PV", "AC_MR_PV")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  tmp.melt <- melt(data = tmp, id = c("time"))
  
  ggplot(data = tmp.melt) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + ggtitle("Total claim amount")

  # Plot AC Personal
  tmp <- predict.df[ predict.df$Type == "Personal", names(predict.df) %in% c("time", "AC_BI", "AC_PD", "AC_COM", "AC_COL", "AC_PI", "AC_CR", "AC_MR", "AC_IS")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  tmp.melt <- melt(data = tmp, id = c("time"))
  
  ggplot(data = tmp.melt) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + ggtitle("Total personal claim amount") 

  # Plot AC Commercial
  tmp <- predict.df[ predict.df$Type == "Commercial", names(predict.df) %in% c("time", "AC_BI", "AC_PD", "AC_COM", "AC_COL", "AC_PI", "AC_CR", "AC_MR", "AC_IS")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  tmp.melt <- melt(data = tmp, id = c("time"))
  
  ggplot(data = tmp.melt) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + ggtitle("Total commercial claim amount") 

  # Plot NC
  tmp <- predict.df[, names(predict.df) %in% c("time", "NC_BI", "NC_PD", "NC_COM", "NC_COL", "NC_PI")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  tmp.melt <- melt(data = tmp, id = c("time"))
  
  ggplot(data = tmp.melt) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + ggtitle("total claims")

    # Plot NC Personal
  tmp <- predict.df[ predict.df$Type == "Personal", names(predict.df) %in% c("time", "NC_BI", "NC_PD", "NC_COM", "NC_COL", "NC_PI")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  tmp.melt <- melt(data = tmp, id = c("time"))
  
  ggplot(data = tmp.melt) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + ggtitle("Total personal claims") 

      # Plot NC Commercial
  tmp <- predict.df[ predict.df$Type == "Commercial", names(predict.df) %in% c("time", "NC_BI", "NC_PD", "NC_COM", "NC_COL", "NC_PI")]
  tmp <- aggregate(formula = . ~ time , data = tmp, FUN = sum)
  tmp.melt <- melt(data = tmp, id = c("time"))
  
  ggplot(data = tmp.melt) + geom_bar(mapping = aes(x = time, y = value, fill = variable) , stat = "identity") + ggtitle("Total commercial claims") 

  tmp <- predict.df[, c("time", "RiskClass", "prop", "Type", "Autonomy")]
  
  ggplot(data = tmp)+ geom_line(mapping = aes(x = time, y = prop, color = RiskClass)) + facet_wrap(. ~ Type + Autonomy, scales = "free")